# Constructions for $A$-Modules

## `RModule(A): AlgMat -> ModRng`

Given a subalgebra $A$ of $M_n(K)$, create the right $A$-module $M$ with underlying vector space $K^{(n)}$, where the action of $a \in A$ is given by $m*a$, $m \in M$.

## `RModule(Q): [ MtrxS ] -> ModTupRng`

Given the subalgebra $A$ of $M_n(K)$ generated by the terms of the sequence $Q$, create the right $A$-module $M$ with underlying vector space $K^{(n)}$, where the action of $a \in A$ is given by $m*a$, $m \in M$.

## `Example: Create K6 (ex-2aced1)`

We construct the $6$-dimensional module over ${\bf F}_{2}$ with an action given by the matrices

$$
\begin{pmatrix}1&0&0&1&0&1\\
   0&1&0&0&1&1\\
   0&1&1&1&1&0\\
   0&0&0&1&1&0\\
   0&0&0&1&0&1\\
   0&1&0&1&0&0\end{pmatrix}\qquad\qquad
   \begin{pmatrix}0&1&1&0&1&0\\
   0&0&1&1&1&1\\
   1&0&0&1&0&1\\
   0&0&0&1&0&0\\
   0&0&0&0&1&0\\
   0&0&0&0&0&1\end{pmatrix}
$$

```magma
> A := MatrixAlgebra<GF(2), 6 |
>   [ 1,0,0,1,0,1,
>     0,1,0,0,1,1,
>     0,1,1,1,1,0,
>     0,0,0,1,1,0,
>     0,0,0,1,0,1,
>     0,1,0,1,0,0 ],
>   [ 0,1,1,0,1,0,
>     0,0,1,1,1,1,
>     1,0,0,1,0,1,
>     0,0,0,1,0,0,
>     0,0,0,0,1,0,
>     0,0,0,0,0,1 ] >;
> M := RModule(A);
> M;
RModule M of dimension 6 over GF(2)

```